This application relates to digital communication where the channel is estimated by pilot symbols. In particular, it relates to situations where it is desirable to avoid or reduce the use of high-order interpolation filters, because of the required memory and complexity for such filters. It also concerns related situations where it is desirable to estimate channel correlation functions by low-complexity methods.
In wireless communications, the data to be communicated is typically transmitted over a channel whose characteristics vary in time and frequency. That is to say, the amplitude and phase of the channel change from one symbol to the next and from one frequency to the next. How much the channel changes between two symbols in time does essentially depend on two things, namely the duration of a symbol and how fast the actual channel is varying, whereas how much the channel changes between two frequencies depends on how far apart the frequencies are and how frequency selective the channel is.
A common way to estimate a varying channel is to insert known symbols in the transmitted sequence, so-called pilot symbols. The pilot symbols might either be distributed as single symbols, or they might be clustered together to form short sequences of symbols. In systems based on orthogonal frequency division multiplexing (OFDM), it is commonplace to transmit scattered pilot symbols on some of the different carriers to aid in channel estimation. This is for instance the case in digital video broadcasting (DVB), where essentially 1 out of 12 transmitted symbols is a pilot. In DVB, pilots are only transmitted on every third carrier, and on those carriers every fourth symbol is a pilot.
One of the design objectives when determining how close the pilots should be in time and frequency is to get good performance without using too many pilots. That is, there should be enough pilots to allow the channel to be estimated with reasonable complexity and to cause only a small performance loss without wasting bandwidth by transmitting unnecessarily many pilots. The placement of pilots in time is essentially determined by the Nyquist sampling theorem, which implies that the channel must be sampled at a frequency at least twice the highest Doppler frequency in order to avoid aliasing. For instance, if the Doppler frequency is 50 Hz, then the channel has to be sampled at a sampling frequency, fS, of 100 Hz, i.e., there must be a pilot symbol every 10 ms. If the symbol duration is, say, 1 ms, this implies that every ten symbols must be a pilot to avoid aliasing.
Just as the Nyquist sampling theorem states that, in time, there is a maximum frequency that can be handled that relates to the sampling frequency, there is an analogous result in the frequency direction, with the theorem stating that there is a maximum duration of the impulse response of the channel that can be handled that relates to the frequency difference, fdist, between samples. This is described in F. Claessen et al., “Channel estimation units for an OFDM system suitable for mobile communication”, ITG Conf. on Mobile Radio, Neu-Ulm, Germany (September 1995). If the duration of the impulse response of the channel is denoted Tm, then Tm must not exceed 1/fdist to avoid aliasing. In the context of channel estimation by interpolation, the sampling points correspond to the pilots or carriers where a channel estimate is already made.
U.S. Patent Application Publication No. US 2003/0012308 to H. Sampath et al. also describes channel estimation by receiving training symbols embedded in data symbols and an adaptive interpolator for generating data channel responses for data symbols by interpolating training channel responses. According to the publication, channel estimation may be adapted according to estimated delay spread. Various aspects of channel estimation in radio systems, including OFDM and DVB systems, are described in U.S. Pat. No. 6,381,290 to Mostafa et al.; U.S. Pat. No. 6,449,245 to Y. Ikeda et al.; and U.S. Pat. No. 6,608,863 to T. Onizawa et al.; International Patent Publication No. WO 02/23840 to R. Weber; Published European Patent Application No. EP 1 296 473 to G. Li et al.; K. Ramusubramanian et al., “An OFDM Timing Recovery Scheme with Inherent Delay-Spread Estimation”, IEEE GLOBECOM '01, vol. 5, pp. 3111-3115 (2001); A. A. Hutter et al., “Channel Estimation for Mobile OFDM Systems”, Proc. IEEE Vehicular Technology Conf., vol. 1, pp. 305-309, Amsterdam, Netherlands (September 1999); and S. Y. Park et al., “Performance Analysis of Pilot Symbol Arrangement for OFDM System under Time-Varying Multi-Path Rayleigh Fading Channels”, IECE Trans. on Communications, vol. E84-B, pp. 36-45 (January 2001).
When performing interpolation for channel estimation, one can in principle use a two-dimensional filter, i.e., operating in time and frequency simultaneously, to get optimum performance. It is, however, much more common in practice to reduce complexity by instead using a one-dimensional filter operating in either time or frequency. Alternatively, two filters can be used in a two-step process, one for interpolation in time and one for interpolation in frequency. When using a two-step approach, the order between time and frequency interpolation is a matter of design choice. Once you have decided to perform the channel estimation in a certain order, say time first and then frequency, the filters can be chosen independently of one another.
Although it in theory is possible to estimate the channel as long as the Nyquist criterion is fulfilled for the time direction and the corresponding requirement for the frequency direction holds, it requires ideal interpolation filters, which is not feasible to implement. Consequently, the pilots are located closer together in time and frequency than theoretically needed in order to allow the use of practical interpolation filters.
For interpolation in time, it will be seen that if the pilots are located such that an interpolation filter of reasonable complexity is suitable for a Doppler frequency of, say, 50 Hz, then a much simpler filter will do when the actual Doppler frequency is much smaller. That is to say, if the maximum Doppler frequency is rarely experienced, then a simpler filter will suffice most of the time, and the power consumption can be reduced by using a filter that is good enough, but not better. A less complex filter implies fewer operations, which also means that the power consumption can be reduced and that the available resources for performing calculations in a receiver can be used for something else.
As will be discussed in more detail below, a more complex interpolation filter operating in time usually also means more buffering. The reason is that the interpolation filter typically is symmetric, so that if for instance a filter of order ten is used, one has to buffer data corresponding to five pilots in order to perform the interpolation. If this kind of complex interpolation filter is needed only for the very highest Doppler frequency, it implies that in most situations one could use much less buffering.
When performing interpolation in frequency, if Tm=1 microsecond (μs), then it suffices to have fdist=1 MHz, but if Tm=100 μs, then fdist must be decreased to 10 kHz. Stated otherwise, if the pilots are placed to handle the situation where Tm=100 μs by using a rather complex interpolation filter, then a considerably less complex filter can be used when Tm=1 μs. Again, a less complex filter implies fewer operations, which also means that the power consumption can be reduced and that the available resources for performing calculations in a receiver can be used for something else.
One specific case where the problem has been seen is in systems based on OFDM when the number of sub-carriers is large, like for instance in DVB. Due to the fact that the number of sub-carriers is large, the symbol duration will also be large, which means that the pilots will be further apart in time if the fraction of symbols used as pilots is kept the same, implying that interpolation becomes harder, thus requiring a more complex filter. Moreover, because the number of sub-carriers is large, the amount of data that has to be buffered per OFDM symbol will also be large. In fact in some cases where DVB has been considered, it has even been stated that because of the buffering only linear interpolation is feasible.
Consequently, there is a need to perform channel estimation using interpolation filters that are properly adjusted depending on the channel conditions. In particular, for interpolation in time, there is a need for filters that can require minimum buffering.